The MXR Dist+ is alright. It's not the best distortion out there. I think the Wylde OD or a Boss SD-1 or Bad Monkey would work much better. You can get a smoother tone with an overdrive versus a distortion. The clipping is totally different between the two types.
Gilbert used Laney's for quite a long time, pretty much all through the 90's and still does I think, although I've seen his face with the Marshall Vintage Modern as of late. He uses his volume control A LOT. I don't know how much you use your volume control on your guitar to vary the push and dynamics, but Paul does that quite a lot. Roll back for some clean, up a little more for mild drive, up all the way for the kick in the head.
Getting great tone doesn't happen over night. You're experimenting and searching for that sound in your head. Thing is, you've got it good because of the internet. You'll probably find it before players my age and older did (I'm 35 BTW) because there was no internet when I started (do I sound old? LOL).